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Jean-François Remacle authoredboundary layers in 2D periodi bug fixed many other stuff JFJean-François Remacle authoredboundary layers in 2D periodi bug fixed many other stuff JF
qualityMeasures.cpp 17.48 KiB
// Gmsh - Copyright (C) 1997-2011 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to <gmsh@geuz.org>.
#include "qualityMeasures.h"
#include "BDS.h"
#include "MVertex.h"
#include "MTriangle.h"
#include "MQuadrangle.h"
#include "MTetrahedron.h"
#include "Numeric.h"
#include "polynomialBasis.h"
#include "GmshMessage.h"
#include <limits>
#include <string.h>
double qmTriangle(const BDS_Point *p1, const BDS_Point *p2, const BDS_Point *p3,
const qualityMeasure4Triangle &cr)
{
return qmTriangle(p1->X, p1->Y, p1->Z, p2->X, p2->Y, p2->Z, p3->X, p3->Y, p3->Z, cr);
}
double qmTriangle(BDS_Face *t, const qualityMeasure4Triangle &cr)
{
BDS_Point *n[4];
t->getNodes(n);
return qmTriangle(n[0], n[1], n[2], cr);
}
double qmTriangle(MTriangle*t, const qualityMeasure4Triangle &cr)
{
return qmTriangle(t->getVertex(0), t->getVertex(1), t->getVertex(2), cr);
}
double qmTriangle(const MVertex *v1, const MVertex *v2, const MVertex *v3,
const qualityMeasure4Triangle &cr)
{
return qmTriangle(v1->x(), v1->y(), v1->z(), v2->x(), v2->y(), v2->z(),
v3->x(), v3->y(), v3->z(), cr);
}
// Triangle abc
// quality is between 0 and 1
double qmTriangle(const double &xa, const double &ya, const double &za,
const double &xb, const double &yb, const double &zb,
const double &xc, const double &yc, const double &zc,
const qualityMeasure4Triangle &cr)
{
double quality;
switch(cr){
case QMTRI_RHO:
{
// quality = rho / R = 2 * inscribed radius / circumradius
double a [3] = {xc - xb, yc - yb, zc - zb};
double b [3] = {xa - xc, ya - yc, za - zc};
double c [3] = {xb - xa, yb - ya, zb - za};
norme(a);
norme(b);
norme(c);
double pva [3]; prodve(b, c, pva); const double sina = norm3(pva);
double pvb [3]; prodve(c, a, pvb); const double sinb = norm3(pvb);
double pvc [3]; prodve(a, b, pvc); const double sinc = norm3(pvc);
if (sina == 0.0 && sinb == 0.0 && sinc == 0.0) quality = 0.0;
else quality = 2 * (2 * sina * sinb * sinc / (sina + sinb + sinc));
}
break;
// condition number case QMTRI_COND:
{
/*
double a [3] = {xc - xa, yc - ya, zc - za};
double b [3] = {xb - xa, yb - ya, zb - za};
double c [3] ; prodve(a, b, c); norme(c);
double A[3][3] = {{a[0] , b[0] , c[0]} ,
{a[1] , b[1] , c[1]} ,
{a[2] , b[2] , c[2]}};
*/
quality = -1;
}
break;
default:
Msg::Error("Unknown quality measure");
return 0.;
}
return quality;
}
double qmTet(MTetrahedron *t, const qualityMeasure4Tet &cr, double *volume)
{
return qmTet(t->getVertex(0), t->getVertex(1), t->getVertex(2), t->getVertex(3),
cr, volume);
}
double qmTet(const MVertex *v1, const MVertex *v2, const MVertex *v3,
const MVertex *v4, const qualityMeasure4Tet &cr, double *volume)
{
return qmTet(v1->x(), v1->y(), v1->z(), v2->x(), v2->y(), v2->z(),
v3->x(), v3->y(), v3->z(), v4->x(), v4->y(), v4->z(), cr, volume);
}
double qmTet(const double &x1, const double &y1, const double &z1,
const double &x2, const double &y2, const double &z2,
const double &x3, const double &y3, const double &z3,
const double &x4, const double &y4, const double &z4,
const qualityMeasure4Tet &cr, double *volume)
{
switch(cr){
case QMTET_ONE:
return 1.0;
case QMTET_3:
{
double mat[3][3];
mat[0][0] = x2 - x1;
mat[0][1] = x3 - x1;
mat[0][2] = x4 - x1;
mat[1][0] = y2 - y1;
mat[1][1] = y3 - y1;
mat[1][2] = y4 - y1;
mat[2][0] = z2 - z1;
mat[2][1] = z3 - z1;
mat[2][2] = z4 - z1;
*volume = fabs(det3x3(mat)) / 6.;
double l = ((x2 - x1) * (x2 - x1) +
(y2 - y1) * (y2 - y1) +
(z2 - z1) * (z2 - z1));
l += ((x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1) + (z3 - z1) * (z3 - z1));
l += ((x4 - x1) * (x4 - x1) + (y4 - y1) * (y4 - y1) + (z4 - z1) * (z4 - z1));
l += ((x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2) + (z3 - z2) * (z3 - z2));
l += ((x4 - x2) * (x4 - x2) + (y4 - y2) * (y4 - y2) + (z4 - z2) * (z4 - z2));
l += ((x3 - x4) * (x3 - x4) + (y3 - y4) * (y3 - y4) + (z3 - z4) * (z3 - z4));
return 12. * pow(3 * fabs(*volume), 2. / 3.) / l;
}
case QMTET_2:
{
double mat[3][3];
mat[0][0] = x2 - x1; mat[0][1] = x3 - x1;
mat[0][2] = x4 - x1;
mat[1][0] = y2 - y1;
mat[1][1] = y3 - y1;
mat[1][2] = y4 - y1;
mat[2][0] = z2 - z1;
mat[2][1] = z3 - z1;
mat[2][2] = z4 - z1;
*volume = fabs(det3x3(mat)) / 6.;
double p0[3] = {x1, y1, z1};
double p1[3] = {x2, y2, z2};
double p2[3] = {x3, y3, z3};
double p3[3] = {x4, y4, z4};
double s1 = fabs(triangle_area(p0, p1, p2));
double s2 = fabs(triangle_area(p0, p2, p3));
double s3 = fabs(triangle_area(p0, p1, p3));
double s4 = fabs(triangle_area(p1, p2, p3));
double rhoin = 3. * fabs(*volume) / (s1 + s2 + s3 + s4);
double l = sqrt((x2 - x1) * (x2 - x1) +
(y2 - y1) * (y2 - y1) +
(z2 - z1) * (z2 - z1));
l = std::max(l, sqrt((x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1) +
(z3 - z1) * (z3 - z1)));
l = std::max(l, sqrt((x4 - x1) * (x4 - x1) + (y4 - y1) * (y4 - y1) +
(z4 - z1) * (z4 - z1)));
l = std::max(l, sqrt((x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2) +
(z3 - z2) * (z3 - z2)));
l = std::max(l, sqrt((x4 - x2) * (x4 - x2) + (y4 - y2) * (y4 - y2) +
(z4 - z2) * (z4 - z2)));
l = std::max(l, sqrt((x3 - x4) * (x3 - x4) + (y3 - y4) * (y3 - y4) +
(z3 - z4) * (z3 - z4)));
return 2. * sqrt(6.) * rhoin / l;
}
break;
default:
Msg::Error("Unknown quality measure");
return 0.;
}
}
double mesh_functional_distorsion(MElement *t, double u, double v)
{
// compute uncurved element jacobian d_u x and d_v x
double mat[3][3];
t->getPrimaryJacobian(u, v, 0, mat);
// t->getJacobian(u,v,0,mat);
double v1[3] = {mat[0][0], mat[0][1], mat[0][2]};
double v2[3] = {mat[1][0], mat[1][1], mat[1][2]};
double normal1[3];
prodve(v1, v2, normal1);
double nn = sqrt(normal1[0]*normal1[0] +
normal1[1]*normal1[1] +
normal1[2]*normal1[2]);
// compute uncurved element jacobian d_u x and d_v x
t->getJacobian(u, v, 0, mat);
double v1b[3] = {mat[0][0], mat[0][1], mat[0][2]};
double v2b[3] = {mat[1][0], mat[1][1], mat[1][2]};
double normal[3];
prodve(v1b, v2b, normal);
double sign = 1.0;
prosca(normal1, normal, &sign);
double det = norm3(normal) * (sign > 0 ? 1. : -1.) / nn;
// printf("%g %g : %g : %g n1 (%g,%g,%g)\n",u,v,sign,det, normal1[0], normal1[1], normal1[2]);
// printf("n (%g,%g,%g)\n", normal[0], normal[1], normal[2]);
return det;}
static double MINQ (double a, double b, double c){
if (a == 0) return std::min(a+b+c,c);
double xmin = -b/(2*a);
if (xmin < 0 || xmin > 1)return std::min(c,a+b+c);
return std::min(c,std::min(a+b+c,a * xmin * xmin + b * xmin + c));
}
double mesh_functional_distorsion_p2_bezier_refined(MTriangle *t)
{
double J1 =mesh_functional_distorsion(t,0.0,0.0);
double J2 =mesh_functional_distorsion(t,1.0,0.0);
double J3 =mesh_functional_distorsion(t,0.0,1.0);
double J4 =mesh_functional_distorsion(t,0.5,0.0);
double J5 =mesh_functional_distorsion(t,0.5,0.5);
double J6 =mesh_functional_distorsion(t,0.0,0.5);
double J36 =mesh_functional_distorsion(t,0.0,.75);
double J35 =mesh_functional_distorsion(t,0.25,.75);
double J56 =mesh_functional_distorsion(t,0.25,.5);
double J16 =mesh_functional_distorsion(t,0.0,.25);
double J14 =mesh_functional_distorsion(t,0.25,.0);
double J46 =mesh_functional_distorsion(t,0.25,.25);
double J45 =mesh_functional_distorsion(t,0.5,.25);
double J52 =mesh_functional_distorsion(t,0.75,.25);
double J24 =mesh_functional_distorsion(t,0.75,.0);
double d[15] = {
J1,J6,J4,2*J16-0.5*(J1+J6),2*J14-0.5*(J1+J4),2*J46-0.5*(J6+J4),
J3,J5,2*J36-0.5*(J3+J6),2*J35-0.5*(J3+J5),2*J56-0.5*(J5+J6),
J2,2*J45-0.5*(J4+J5),2*J52-0.5*(J5+J2),2*J24-0.5*(J2+J4)};
return *std::min_element(d,d+15);
}
double mesh_functional_distorsion_p2_exact(MTriangle *t)
{
double J1 =mesh_functional_distorsion(t,0.0,0.0);
double J2 =mesh_functional_distorsion(t,1.0,0.0);
double J3 =mesh_functional_distorsion(t,0.0,1.0);
double J4 =mesh_functional_distorsion(t,0.5,0.0);
double J5 =mesh_functional_distorsion(t,0.5,0.5);
double J6 =mesh_functional_distorsion(t,0.0,0.5);
const double a = J1;
const double b = -3*J1-J2+4*J4;
const double c = -3*J1-J3+4*J6;
const double d = 4*(J1-J4+J5-J6);
const double e = 2*(J1+J2-2*J4);
const double f = 2*(J1+J3-2*J6);
double js[3] = {
MINQ (2*(J1+J2-2*J4), -3*J1-J2+4*J4, J1),
MINQ (2*(J1+J3-2*J6), -3*J1-J3+4*J6, J1),
MINQ (2*(J3+J2-2*J5), -3*J2-J3+4*J5, J2)
};
double min_interm = *std::min_element(js,js+3);
double mat[2][2] = {{2*e,d},{d,2*f}};
double x[2], rhs[2] = {-b,-c};
if (!sys2x2(mat,rhs,x))return min_interm;
const double ximin = x[0];
const double etamin = x[1];
if (ximin> 0 && etamin > 0 && 1-ximin-etamin>0){
const double m4 = a+b*ximin+c*etamin+d*ximin*etamin+
e*ximin*ximin + f*etamin*etamin;
/*
if (m4 < min_interm && (m4 < .9 || m4 > 1.1)){
printf("m4 = %g xi = %g eta = %g min_interm = %g min_edges = %g %g %g\n",m4,ximin,etamin,min_interm, MINQ (e,b,a), MINQ (f,c,a), MINQ (-d+e+f,b-c+d-2*f,a+c+f));
FILE *f = fopen ("t.pos","w");
fprintf(f,"ST2(%g,%g,0,%g,%g,0,%g,%g,0,%g,%g,0,%g,%g,0,%g,%g,0){%g,%g,%g,%g,%g,%g}\n",
t->getVertex(0)->x(),t->getVertex(0)->y(),
t->getVertex(1)->x(),t->getVertex(1)->y(),
t->getVertex(2)->x(),t->getVertex(2)->y(),
t->getVertex(3)->x(),t->getVertex(3)->y(),
t->getVertex(4)->x(),t->getVertex(4)->y(),
t->getVertex(5)->x(),t->getVertex(5)->y(),
J1,J2,J3,J4,J5,J6);
fclose(f);
getchar();
}
*/
return std::min(m4, min_interm);
}
return min_interm;
}
double mesh_functional_distorsion_pN(MElement *t)
{
const bezierBasis *jac = t->getJacobianFuncSpace()->bezier;
fullVector<double>Ji(jac->points.size1());
// printf("%d points for bez \n",jac->points.size1());
for (int i=0;i<jac->points.size1();i++){
double u = jac->points(i,0);
double v = jac->points(i,1);
// JF : bezier points are defined in the [0,1] x [0,1] quad
if (t->getType() == TYPE_QUA){
u = -1 + 2*u;
v = -1 + 2*v;
}
Ji(i) = mesh_functional_distorsion(t,u,v);
// printf("J(%g,%g) = %12.5E\n",u,v,Ji(i));
}
fullVector<double> Bi( jac->matrixLag2Bez.size1() );
jac->matrixLag2Bez.mult(Ji,Bi);
/*
jac->matrixLag2Bez.print("Lag2Bez");
jac->points.print("Points");
t->getFunctionSpace(t->getPolynomialOrder())->points.print("lagrangianNodes");
t->getFunctionSpace(t->getPolynomialOrder())->monomials.print("Monomials");
t->getFunctionSpace(t->getPolynomialOrder())->coefficients.print("Coefficients");
*/
return *std::min_element(Bi.getDataPtr(),Bi.getDataPtr()+Bi.size());
}
double qmDistorsionOfMapping (MTriangle *e)
{
// return 1.0;
if (e->getPolynomialOrder() == 1) return 1.0;
else if (e->getPolynomialOrder() == 2) {
// const double exact = mesh_functional_distorsion_p2_exact(e);
const double bezier= mesh_functional_distorsion_pN(e);
// if (bezier < .1){
// const double bezier_refined= mesh_functional_distorsion_p2_bezier_refined(e);
// return bezier_refined;
// }
/* if (exact < .99 || exact > 1.01){
FILE *f = fopen ("statistics.dat","a");
fprintf(f,"%12.5E %12.5E %12.5E\n",exact,bezier,bezier_refined);
fclose(f);
if (exact > 0 && bezier < 0){
f = fopen ("t.pos","w");
double J1 =mesh_functional_distorsion(e,0.0,0.0);
double J2 =mesh_functional_distorsion(e,1.0,0.0);
double J3 =mesh_functional_distorsion(e,0.0,1.0);
double J4 =mesh_functional_distorsion(e,0.5,0.0);
double J5 =mesh_functional_distorsion(e,0.5,0.5);
double J6 =mesh_functional_distorsion(e,0.0,0.5);
fprintf(f,"ST2(%g,%g,0,%g,%g,0,%g,%g,0,%g,%g,0,%g,%g,0,%g,%g,0){%g,%g,%g,%g,%g,%g}\n",
e->getVertex(0)->x(),e->getVertex(0)->y(),
e->getVertex(1)->x(),e->getVertex(1)->y(),
e->getVertex(2)->x(),e->getVertex(2)->y(),
e->getVertex(3)->x(),e->getVertex(3)->y(),
e->getVertex(4)->x(),e->getVertex(4)->y(),
e->getVertex(5)->x(),e->getVertex(5)->y(),
J1,J2,J3,J4,J5,J6);
fclose(f);
getchar();
}
}
*/
return bezier;
}
else return mesh_functional_distorsion_pN(e);
}
double qmDistorsionOfMapping (MQuadrangle *e)
{
// return 1.0;
if (e->getPolynomialOrder() == 1) return 1.0;
else return mesh_functional_distorsion_pN(e);
}
static double mesh_functional_distorsion(MTetrahedron *t, double u, double v, double w)
{
// compute uncurved element jacobian d_u x and d_v x
double mat[3][3];
t->getPrimaryJacobian(u, v, w, mat);
const double det1 = det3x3(mat);
t->getJacobian(u, v, w, mat);
const double detN = det3x3(mat);
if (det1 == 0 || detN == 0) return 0;
double dist = det1 / detN;
return dist;
}
double qmDistorsionOfMapping(MTetrahedron *t)
{
const bezierBasis *jac = t->getJacobianFuncSpace()->bezier;
fullVector<double>Ji(jac->points.size1());
for (int i=0;i<jac->points.size1();i++){
const double u = jac->points(i,0);
const double v = jac->points(i,1);
const double w = jac->points(i,2);
Ji(i) = mesh_functional_distorsion(t,u,v,w);
}
fullVector<double> Bi( jac->matrixLag2Bez.size1() );
jac->matrixLag2Bez.mult(Ji,Bi);
return *std::min_element(Bi.getDataPtr(),Bi.getDataPtr()+Bi.size());
}
double qmTriangleAngles (MTriangle *e) { double a = 500;
double worst_quality = std::numeric_limits<double>::max();
double mat[3][3];
double mat2[3][3];
double den = atan(a*(M_PI/9)) + atan(a*(M_PI/9));
// This matrix is used to "rotate" the triangle to get each vertex
// as the "origin" of the mapping in turn
double rot[3][3];
rot[0][0]=-1; rot[0][1]=1; rot[0][2]=0;
rot[1][0]=-1; rot[1][1]=0; rot[1][2]=0;
rot[2][0]= 0; rot[2][1]=0; rot[2][2]=1;
double tmp[3][3];
double minAngle = 120.0;
for (int i = 0; i < e->getNumPrimaryVertices(); i++) {
const double u = i == 1 ? 1 : 0;
const double v = i == 2 ? 1 : 0;
const double w = 0;
e->getJacobian(u, v, w, mat);
e->getPrimaryJacobian(u,v,w,mat2);
for (int j = 0; j < i; j++) {
matmat(rot,mat,tmp);
memcpy(mat, tmp, sizeof(mat));
}
//get angle
double v1[3] = {mat[0][0], mat[0][1], mat[0][2] };
double v2[3] = {mat[1][0], mat[1][1], mat[1][2] };
double v3[3] = {mat2[0][0], mat2[0][1], mat2[0][2] };
double v4[3] = {mat2[1][0], mat2[1][1], mat2[1][2] };
norme(v1);
norme(v2);
norme(v3);
norme(v4);
double v12[3], v34[3];
prodve(v1,v2,v12);
prodve(v3,v4,v34);
norme(v12);
norme(v34);
double orientation;
prosca(v12,v34,&orientation);
// If the triangle is "flipped" it's no good
if (orientation < 0)
return -std::numeric_limits<double>::max();
double c;
prosca(v1,v2,&c);
double x = acos(c)-M_PI/3;
double angle = (x+M_PI/3)/M_PI*180;
double quality = (atan(a*(x+M_PI/9)) + atan(a*(M_PI/9-x)))/den;
worst_quality = std::min(worst_quality, quality);
// minAngle = std::min(angle, minAngle);
// printf("Angle %g ", angle);
// printf("Quality %g\n",quality);
}
// printf("MinAngle %g ", minAngle);
// printf("\n");
// return minAngle;
return worst_quality;
}
double qmQuadrangleAngles (MQuadrangle *e) {
double a = 100;
double worst_quality = std::numeric_limits<double>::max();
double mat[3][3];
double mat2[3][3]; double den = atan(a*(M_PI/4)) + atan(a*(2*M_PI/4 - (M_PI/4)));
// This matrix is used to "rotate" the triangle to get each vertex
// as the "origin" of the mapping in turn
double rot[3][3];
rot[0][0]=-1; rot[0][1]=1; rot[0][2]=0;
rot[1][0]=-1; rot[1][1]=0; rot[1][2]=0;
rot[2][0]= 0; rot[2][1]=0; rot[2][2]=1;
//double tmp[3][3];
const double u[9] = {-1,-1, 1, 1, 0,0,1,-1,0};
const double v[9] = {-1, 1, 1,-1, -1,1,0,0,0};
for (int i = 0; i < 9; i++) {
e->getJacobian(u[i], v[i], 0, mat);
e->getPrimaryJacobian(u[i],v[i],0,mat2);
//for (int j = 0; j < i; j++) {
// matmat(rot,mat,tmp);
// memcpy(mat, tmp, sizeof(mat));
//}
//get angle
double v1[3] = {mat[0][0], mat[0][1], mat[0][2] };
double v2[3] = {mat[1][0], mat[1][1], mat[1][2] };
double v3[3] = {mat2[0][0], mat2[0][1], mat2[0][2] };
double v4[3] = {mat2[1][0], mat2[1][1], mat2[1][2] };
norme(v1);
norme(v2);
norme(v3);
norme(v4);
double v12[3], v34[3];
prodve(v1,v2,v12);
prodve(v3,v4,v34);
norme(v12);
norme(v34);
double orientation;
prosca(v12,v34,&orientation);
// If the if the triangle is "flipped" it's no good
// if (orientation < 0)
// return -std::numeric_limits<double>::max();
double c;
prosca(v1,v2,&c);
// printf("Youhou %g %g\n",c,acos(c)*180/M_PI);
double x = fabs(acos(c))-M_PI/2;
double quality = (atan(a*(x+M_PI/4)) + atan(a*(2*M_PI/4 - (x+M_PI/4))))/den;
worst_quality = std::min(worst_quality, quality);
}
return worst_quality;
}